Machine-learning strategies for testing patterns of morphological variation in small samples: sexual dimorphism in gray wolf (Canis lupus) crania

Background Studies of mammalian sexual dimorphism have traditionally involved the measurement of selected dimensions of particular skeletal elements and use of single data-analysis procedures. Consequently, such studies have been limited by a variety of both practical and conceptual constraints. To compare and contrast what might be gained from a more exploratory, multifactorial approach to the quantitative assessment of form-variation, images of a small sample of modern Israeli gray wolf (Canis lupus) crania were analyzed via elliptical Fourier analysis of cranial outlines, a Naive Bayes machine-learning approach to the analysis of these same outline data, and a deep-learning analysis of whole images in which all aspects of these cranial morphologies were represented. The statistical significance and stability of each discriminant result were tested using bootstrap and jackknife procedures. Results Our results reveal no evidence for statistically significant sexual size dimorphism, but significant sex-mediated shape dimorphism. These are consistent with the findings of prior wolf sexual dimorphism studies and extend these studies by identifying new aspects of dimorphic variation. Additionally, our results suggest that shape-based sexual dimorphism in theC. lupuscranial complex may be more widespread morphologically than had been appreciated by previous researchers. Conclusion Our results suggest that size and shape dimorphism can be detected in small samples and may be dissociated in mammalian morphologies. This result is particularly noteworthy in that it implies there may be a need to refine allometric hypothesis tests that seek to account for phenotypic sexual dimorphism. The methods we employed in this investigation are fully generalizable and can be applied to a wide range of biological materials and could facilitate the rapid evaluation of a diverse array of morphological/phenomic hypotheses.